Designed for courses in advanced calculus and introductory real analysis, Elementary Classical Analysis strikes a careful balance between pure and applied mathematics with an emphasis on specific techniques important to classical analysis without vector calculus or complex analysis. Intended for students of engineering and physical science as well as of pure mathematics.
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About the Author
JERROLD E. MARSDEN, University of California, Berkeley, USA.
--This text refers to an alternate
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Most Helpful Customer Reviews
12 of 12 people found the following review helpful:
4.0 out of 5 stars
Reasonable textbook, some editions full of typos,
By Fab (Stanford, California, USA) - See all my reviews
This review is from: Elementary Classical Analysis (Hardcover)
The good part: The text contains the usual definitions, theorems and proofs in a spacious layout (LaTeX - what would you expect...), and also provides some intuition and insight (with pictures of open and closed sets, sin(1/x) etc). The main text is quite long (some find it too verbose, I liked it), and proofs are given after the main text, and don't clutter the exposition. There are also many worked examples, and exercises (with hints/solutions for odd numbered ones).However, the book (in its 2nd edition, 7th printing) is riddled with typos. And these are not only the occasional harmless typo, no, there are errors at the heart of definitions and proofs. For example, when defining the limes inferior, the sign on infinity is wrong for degenerate cases. Confusing! The proof that Q is countable is wrong, too (though this is trivial to see, so no confusion here.) Lamentably, this is no isolated case. There are about 36 (!) typos on the first 100 pages of the 7th printing (check the author's homepage for a list of errata). This is really too much for a such an expensive "elementary" textbook. However, apparently there is a new printing as of May 2003 that fixes most of these problems. So, make sure you don't accidentally buy an old printing of this second edition.
10 of 10 people found the following review helpful:
5.0 out of 5 stars
Loved it as a student and as a professor,
By
This review is from: Elementary Classical Analysis (Hardcover)
This was my favorite book as an undergraduate student and I've taught from it as a professor. It is an excellent geometric approach to analysis. It can even help students who have difficulty with epsilon delta proofs understand the geometric intuition behind them. The construction of the real line at the beginning is daunting for students who aren't clear about set theory and sequences already but a few supplementary materials can help the students out there (see my webpage notes on real analysis for example). The proofs are hidden which makes it a challenge for students to try prove everything themsleves before peeking at them, but they are available. Just remember to tell your students where they are!
As a student I loved the book because it allowed me to learn everything on the metric space level while allowing students who prefer to stay in Euclidean space to do that. Now I am a metric geometer.
10 of 10 people found the following review helpful:
5.0 out of 5 stars
very helpful book,
By Manhatã "reader618" (New York City, USA) - See all my reviews
This review is from: Elementary Classical Analysis (Hardcover)
I am using this book to teach myself analysis. Because my mathematical background is limited, I cannot assess what the book is missing, or whether alternative methods of presentation would be more insightful. But in terms of clarity and comprehensibility, the book does very well. The authors write very carefully and are not cryptic; the proofs and examples are well-presented, and I rarely feel lost. The book is rigorous but not, let's say, snobbish. I am learning a lot from it.
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